Electrical

ELT-114 Electrical Essentials & Networks Page 48 We can see that the two remaining resistances, R1 and R(comb) are connected together in a “SERIES” combination and again they can be added together (resistors in series) so that the total circuit resistance between points A and B is therefore given as: R(ab) = Rcomb + R1 = 6Ω + 6Ω = 12Ω Total Current = = 12 12 = 1 Problem # 1 Find the equivalent resistance in the following circuits. Part (a) (a) 5 A 50 60 B 5 10 10 Fig.2.22 Circuit for problem # 1 Solution: The equivalent resistance of 5Ω and 5Ω parallel combination is evaluated and the equivalent resistance of parallel combination of 10Ω and 10Ω is evaluated.

ELT-114 Electrical Essentials & Networks Page 49 10 2.5 A B 60 50 5 Requ 2 Req 1 Fig.2.22 (B) Circuit for problem # 1 Now 50 Ω and 5 Ω are in series so their equivalent is 55Ω, 2.5 60 A B 55 Fig.2.22 (c) Circuit for problem # 1 Now 60 Ω and 55 Ω are in Parallel so their equivalent is, 28.7 A B 31.205 2.5 A B Fig.2.22 (D) Circuit for problem # 1 So the equivalent resistance is 31.205Ω Part (b) equ1 equ2 5 5 25 R 2.5 5 5 10 10 10 100 R 5 10 10 20 R 5 50 55 equ3

ELT-114 Electrical Essentials & Networks Page 50 A 20 10 40 30 B Fig.2.23 Circuit for problem # 1 part (B) Solution: In the figure 10Ω and 20Ω are in Parallel and 30 Ω and 40 Ω are in parallel. B 20 10 40 30 A B A Fig.2.23 (B) Circuit for problem # 1 part (B) 23.812 So R = 23.812 A B A B Fig.2.23 (c) Circuit for problem # 1 part (B) 20 10 200 6.67 20 10 30 30 40 1200 17.14 30 40 70 23.812So R = 23.812 AB A B 23.812So R = 23.812 AB A B

ELT-114 Electrical Essentials & Networks Page 51 Part (c) 2 2 = Req 1 A 4 2 B 4 4 Fig.2.24 Circuit for problem # 1 part(c) Resistances 2Ω and 2Ω are in series and their equivalent is 4Ω, so we get; 4 B A 4 2 2 = Req 2 Fig.2.4 (B) Circuit for problem # 1 part (c) 4Ω and 4Ω are in parallel and their equivalent is 2Ω and resistances 2Ω and 2Ω are in series and their equivalent is 4Ω and so we get; 4 2 = Req 3 A B Fig.2.24 (c) Circuit for problem # 1 part (c) Problem# 2 Find the current and voltage drop across each resistance in the circuit shown in Fig.2.5 23.812So R = 23.812 AB A B 23.812So R = 23.812 AB A B 23.812So R = 23.812 AB A B 23.812So R = 23.812 AB A B

ELT-114 Electrical Essentials & Networks Page 52 + – I 24V I3 I4 I2 I1 12 6 4 12 8 I2 I5 I6 Fig.2.2.5 Circuit for problem # 2 Solution: Requ1 = 6 × 12 6+12 = 4 Ω Requ2 = 4 × 8 4+8 = 2.6 Ω Equivalent Resistance of Requ1 and Requ2 is Requ = 4 + 2.6 = 6.6 Ω I + – 24V I2 I1 12 12 + – 24V I2 I1 6.66 Fig.2.25 (B) Circuit for problem # 2 So the current is; Using current division rule find currents I1 and I2so, I1= 6.66 12+6.66 × 5.595 I2 = 6.66 18.66 × 5.595 = 1.996 Amp Voltage across 6.66 and 12 ohm resistor is same as applied voltage (parallel circuit). Problem # 3 equ 6.66x12 79.92 R 4.289 6.66 12 18.66 equ V 24 I 5.595 Amp R 4.289 R=4 Ω R=2.6 Ω

ELT-114 Electrical Essentials & Networks Page 53 A circuit consists of two resistors R1 and R2 which are connected in series and current of 2mA is flowing through it. Applied voltage is 24 V. Fid the value of R2=1 R1 R2 2mA 1K 24 + – Fig.2.26 Circuit for problem # 3 Solution: R1=? R2= 1KΩ V=24 Volts I= 2mA By Ohm’s law V= I Requ Requ = V I = 24 2x10−3 = 12 KΩ R1 = Requ – R2 = 12 KΩ – 1 KΩ R1 = 11 KΩ Problem # 4 In the circuit shown 2.7, the current flowing through 10 Ω resistors is 0.5 Amp and the total current taken from the voltage source is 2 Amp. (i) Current passing through the remaining resistors. (ii) The value of the unknown resistor X I1 I y I 2 I 3 0.5A 10 20 30 2Amp X Fig.2.27 Circuit for problem # 4 Solution: Let R1 = 10Ω

ELT-114 Electrical Essentials & Networks Page 54 I1 = 0.5 Amp Voltage drop across R1that is VR1 = I1× R1 = 0.5 x 10 = 5 volts R2 = 20Ω R3 = 30Ω R1, R2, R3and RX are connected in parallel VR1 = VR2 = VR3 = VX = 5 volts I2 = 5 20 = 0.25 Amp I3 = 5 30 =0.1666 Amp IX = 2–I1 – I2 – I3 IX =2 – 0.5 – 0.25 – 0.1666 IX =1.5834 Amp X or RX = V Ix = 5 1.5834 Unknown resistance X = 3.577 Ω Cells in Series: In a series connection, batteries of like voltage and amp-hour capacity are connected to increase the voltage of the overall assembly. The positive terminal of the first battery is connected to the negative terminal of the second battery and so on, until the desired voltage is reached. Cells in series Cells in Parallel: In a parallel connection, batteries of like voltages and capacities are connected to increase the capacity of the overall assembly. The positive terminals of all batteries are connected together, or to a common conductor, and all negative terminals are connected in the same manner.

ELT-114 Electrical Essentials & Networks Page 55 Cells in Parallel 2.2.11 POWER AND ENERGY: Electric Power The rate of doing work is called as Power. In other words we can say the rate at which energy is used is called as Power. It is represented by P. mathematically, Power = Energy Time P = W t = V × Q t = V × I × t t (As Q=I×t) P = V I Other formula of electric power P = I 2 R P = 2 Energy "The capability of doing work of a body is called as energy." There are different forms of energy and these are interring convertible. For example chemical energy, electric energy, and mechanical energy, Energy and work are same quantities. The unit of energy is Joule. If the amount of the charge is Q and is moved in a potential difference V volts then energy or work done (W) can be found by using the following relation. Work Done = Volts x Change W = V x Q 2.2.12 UNITS OF POWER AND ENERGY: Unit of Power: The unit of power is watt. It is defined as if 1 Joule of work is done in one second then the power consumed is 1 watt.

ELT-114 Electrical Essentials & Networks Page 56 1 Watt = 1 Joule/Second Unit of Energy: In electrical engineering energy is defined as: "When a charge of one coulomb is moved in a potential difference of one volt then the amount of the work done on the charge is the energy spent and will be 1 Joule". 1 Joule = 1 Volts × 1 Coulomb 2.2.13 POWER DISSIPATION IN RESISTORS: Any resistor in a circuit that has a voltage drop across it dissipates electrical power. This electrical power is converted into heat energy hence all resistors have a power rating. This is the maximum power that can be dissipated from the resistor without it burning out. The rate of conversion is the power of dissipation. Using the formula for electrical power: . but and thus substituting in the equation for electrical power . This also works substituting = , giving = 2 . Problem Calculate the power dissipated in a 10k resistor with a 5mA current through the resistor. = 2 = (5 × 10−3 ) 2 × (10 × 103 ) P = 250 m W 2.3 KIRCHHOFF’S LAW: Kirchhoff's Laws are used for the analysis of circuits. Finding the unknown values of currents and voltages through all the resistors or components (or branches) in a circuit is called as Analysis of the circuit. When a resistor network comprise of a single power source, Ohm's Law and series & parallel simplification principles are used to analyze the circuit. However when a circuit consists of more than one sources (either voltage or current) only Ohm's law and series parallel simplification are not sufficient to analyze the circuit. We use Kirchhoff's Laws. There are two Kirchhoff's Laws. (i) Kirchhoff's current Law. (ii) Kirchhoff's voltage Law. Kirchhoff's Current Law This law states that:

ELT-114 Electrical Essentials & Networks Page 57 "The algebraic sum of all the current meeting at a node (junction of resistors) is zero." Suppose three resistors R1, R2 and R3 connected as shown in figure below. I 1 I 2 I 3 R1 R2 R3 J Fig.2.28 Circuit for Kirchhoff’s Current Law Current I1 is flowing towards the junction J and currents I2 and I3 are moving out from the junction J. The direction of current towards a node may be considered as positive and the currents leaving the node may be assumed negative (It is arbitrary). I1 – I2 – I3 =0 Or I1 = I2 + I3 The analysis of the circuit based on Kirchhoff's current law is called as Node Analysis. Kirchhoff's Voltage Law (KVL): "This law states that the algebraic sum of all the voltages in a closed loop is zero. Consider a simple circuit comprising of three resistors R1, R2 and R3 powered with V. Fig.2.29 Circuit for Kirchhoff’s voltage Law The sign I is current flowing through the circuit. The point at which current enters a resistor is taken +Ve (positive) and the point at which is leaving is considered as –Ve (Negative). A voltage drop from +Ve to –Ve is taken as negative. So apply KVL while moving clockwise from supply to cover all the components. + V – VR1 – VR2 – VR3 = 0 VR1 + VR2 + VR3 = V ( I × R1 ) + ( I × R2 ) + ( I × R3 ) = V Where “IR” voltage drop

ELT-114 Electrical Essentials & Networks Page 58 The analysis of the circuit based on Kirchhoff's voltage Law is called as Loop/ Mesh analysis. Problems Using Kirchhoff's Current Law Node Analysis Kirchhoff's current law is used to find the unknown currents and voltages in a circuit and the technique is called as Node Analysis. Following steps are used to solve the circuit based on node analysis. i. Find out the number of nodes in the circuit i.e. the junction of two or more resistances. ii. The node of maximum resistances is called as reference node and its potential is considered to be 0 V. iii. Name the voltage at other nodes as VA, VB etc. iv. Assume the currents at node 1, 2, 3 etc as I1, I2, and I3... v. Apply KCL for the no. of nodes present in the circuit. vi. We find equation in the form of node voltages VA, VB etc. vii. Solve the equation and get value, of VA, VB etc. viii. Substitute these values in I1, I2, I3... to find their values. ix. Any –Ve value of the current obtained after calculation shows that current will flow in the opposite direction to the assumed and redraw the circuit. x. Find the values of voltage drops using Ohm's law V = I × R. Problem# 1 Find the currents and voltages across each resistance of the circuit shown below-using KCL (Node Analysis). R1 R2 + – + – 1 2 R = 12 3 8 4 24V 12V I1 I 3 I 2 Fig.2.28 Circuit for problem # 1 Solution: i. There are two nodes in the circuit i.e. 1 & 2. ii. Consider node No. 2 as reference node iii. Suppose the currents as I1, I2, and I3 and all flowing out of the node 1 as shown below: R1 R2 VR1 V + – R3 VR2 VR3 + – + – + – I Figure 2.28

ELT-114 Electrical Essentials & Networks Page 59 R1 R2 + – + – 1 2 R = 12 3 8 4 24V 12V I1 I 3 I 2 Fig.2.28 (B) Circuit for problem #1 iv. Consider the node. 1 voltage VA. v. Apply KCL at node 1. (-Ve shows that direction is opposite to the assumed one). So redraw the circuit R1 R2 + – + – 1 2 R = 12 3 8 4 24V 12V I1 I 3 I 2 Fig.2.28 (C) Circuit for problem # 1 1 2 3 I I I 0 A A A 1 2 3 V – 24 V – 0 V – 12 0 R R R V – 24 V V – 12 A A A 0 4 8 12 6(V – 24) 3V 2(V 12) 0 A A A 6V – 144 3V 2V 24) 0 A A A 11V 168 0 A A 168 V 15.27volts 11 A 1 V 24 15.27 27 8.727 I 4 4 4 1 I 2.18 Amps V I R 2.18x4 8.72Volts R1 1 1 A 2 V 0 15.27 I 1.908Amps 8 8 A 3 V 12 15.27 12 I 0.2725 Amps 12 12 V I xR 0.2725x12 3.27 Volts R3 3 3

ELT-114 Electrical Essentials & Networks Page 60 Problem # 2 (SELF TEST) Find the voltage and currents in all the branches of the circuit shown in figure below using KCL (Node Analysis). R1 + R2 – + – R3 84V 21V 3 6 9 Fig.2.29 Circuit for problem # 2 Problem # 3 (Self Test) Find the currents and voltage across all the elements of the circuit shown below using Kirchhoff's current law. + – + 24V – 30V 4 12 3 Fig.2.30 Circuit for Problem # 3 Problem # 4(Self Test) Find the currents and voltages across all the elements shown in figure below using Kirchhoff's current laws. + – + 12V – 20V R1 50 R = 20 3 20 R2 Fig.2.31 Circuit for problem # 4 Loop /Mesh Analysis: i. In order to solve the circuit using loop/mesh analyses following steps are followed. ii. Assign loop currents say I1, I2, I3 etc. iii. Apply KVL for the individual loops. iv. We get a set of simultaneous equations involving I1, I2 etc. v. Solve the simultaneous equation and get the values of I1, I2 vi. Now find the currents in each branch as assigned in the KVL equations.

ELT-114 Electrical Essentials & Networks Page 61 vii. Calculate the voltage drops using V = IR and powers by P = I²R if required. Problem# 1 Using Kirchhoff's voltage law (Loop mesh analysis) find the currents and voltage across each resistance of the circuit shown below: R1 6V 2 I 1 4 I 2 8 R2 12V + – + – R3 + – + – Fig.2.33 Circuit for problem # 1 Solution: Let I1and I2 be the loop currents assigned to loop 1 and 2. Apply KVL for the loop No. 1 _____(1) Apply KVL for loop.2 Solving 1 & 2 Put I2 in equation. (1) 11 1 2 1 1 2 V.D 0 6 R I R2(I I ) 0 6 2I 4(I I ) 0 6 2I 4I 4I 0 1 1 2 1 2 6I 4I 6 12 4(I I ) 8I 0 2 1 2 12 4I 4I 8I 0 2 1 2 4I 12I 12 1 2 1 2 1 2 2 1 2 12I 8I 12 2 3 12I 36I 36 Adding 24I 48 2 24 I 1Amp 24 6I 4x 1 6 1 6I 10 1 1 10 5 I 1.667 Amp 6 3

ELT-114 Electrical Essentials & Networks Page 62 Current through Current through Current through Problem: 2 Using Kirchhoff's voltage law, find the value of the unknown resistance R shown in figure below the value of the current is 2Amp. R1 R 1 24V + – R2 2 2Amp Fig.2.33 Circuit for problem # 2 Solution: Apply KVL for the circuit shown above. Problem# 3 SELF TEST Find the currents, voltage and power drops across each resistance of the circuit shown below using Kirchhoff's voltage law. R I 1.667 Amp 1 1 V I R 1.667 2 3.3334volts R1 1 1 2 1 2 5 5 R I I 1 1 3 3 R2 2 8 V x4 Volts 3 3 R I 1Amp 3 2 V I xR 1x8 8 Volts R3 3 3 V.D 0 24 IR IR IR 0 1 2 24 21 2xR 2x2 0 24 2 2R 4 0 18 2R 0 2R 18 R 9

ELT-114 Electrical Essentials & Networks Page 63 + – + – 6V 12V 3 2 6 Fig.2.34 Circuit for problem # 3 Problem# 4 (SELF TEST) Find the currents and voltage drop across each element of the circuit shown below using Kirchhoff's voltage law (loop analysis). + – + – 84V 21V 12 3 6 Fig.2.35 Circuit for problem # 4 Problem# 5 Find the current and voltage drop across each resistance of the circuit shown below using Kirchhoff's voltage law. + – + – 12V 24V 2 1 R1 R2 I Fig.2.36 Circuit for problem #5 Solution: Apply KVL of the circuit shown in figure. 24 2I 12V 1xI 0 24 3I 12 0 36 3I 0 3I 36 I 12Amp V IR 12x1 12volts R1 1

ELT-114 Electrical Essentials & Networks Page 64 Problem# 6 (SELF TEST) Using KVL (loop/mesh analysis) find the value of currents and voltage drops across all the elements of the circuit shown in Fig2.37: + – + –6V 12V 2 1 5 3 4 6 Fig.2.37 Circuit for problem #6 2.4 RESISTORS: 2.4.1Resistance Opposition to the flow of current is called as resistance. It is represented by R and denoted by the symbol Ω. The unit of resistance is Ohm. Resistances of different materials are different and depend on the nature of the material. Metals have low resistance and are good conductors. Resistor A component that produces an opposition to the flow of current is called as Resistor. 2.4.2 TYPES OF RESISTORS: Resistors can be divided into two major types: (i) Linear Resistor: These are the resistors in which the current is directly proportional to applied voltage. In such resistors the values of the resistance does not change with applied voltage and temperatures. (ii) Non-Linear Resistors: These are the resistors in which the value of the resistance changes with the applied voltage and temperature or current and voltage have no specific relation. Linear and non-Linear resistor can be divided into following types: V IxR 12x2 24volts R2 2 R

ELT-114 Electrical Essentials & Networks Page 65 Resistors Linear Non Linear Thermistors Photo resistors Fixed Variable Varisters Potentiometer Rheostate Trimmers Carbon Composition Wire wound Thin Film Thick film Carbon film Metal film Metal oxide Cermet film Fusible Fig.2.38 The resistor tree Fixed Resistors These are the resistors whose values do not change and are fixed during their production. There are different types of fixed resistors (i) Carbon Composition Resistors A mixture of finely ground carbon or graphite mixed with a binder in a definite proportion is used to fabricate a desired resistance. These resistors are made in the form of rods and at the two ends of the resistors are joined to metal. Leads are taken out for connection and soldering purposes. These are made in different ratings and values up to 22 mega Ohm and 1/10 watts to 2 watts. These are designed to carry small currents. Fig.2.39 Carbon Composition Resistor (ii) Wire Wound Resistors Wire wound resistors are made by winding a resistance wire which is made of nichrome (Combination of chromium and nickel) on insulating case of materials like Bakelite. In order to protect the wire are covered with inorganic cement. These are available in power ratings of 1 watt to 10 watts with values 1Ω to 200kΩ, tolerance of 5% to 10% and operating temperature

ELT-114 Electrical Essentials & Networks Page 66 up to 350C°. These resistors are low in noise, good time stability, costly and not useful for high frequency. Fig.2.40 Wire Wound Resistor (iii) Thin film Resistors: Thin film resistors are produced by depositing a very thin layer of conducting material on an insulated rod, tube or place which is made of ceramic material or glass. Thin film resistors further can be divided into two groups. Fig.2.41Thin film Resistor (a) Carbon Film Resistors: Carbon film resistors are made by depositing a thin film of carbon on an insulating high grade ceramic rod.

ELT-114 Electrical Essentials & Networks Page 67 Fig.2.42carbon film Resistor These resistors have very low noise, good time stability and wide operating range. (b) Metal film Resistors Metal film resistors are made by depositing a film of a metal or metal alloy on an insulating rod. Fig.2.43Metal film Resistor These are very small in size and are very regicide, have very low noise level and high stability. (iv) Thick Film Resistors Thick film resistors are made with the techniques which are similar to the thin film resistors except that a thick film is deposited in place of thin film. Thick film resistors can be of following types. (a) Metal Oxide Resistors Metal oxide resistors are manufactured by oxidizing tin chloride on a heated glass rod. These resistors are available in high voltage ratings with wide range of values. Metal oxide resistors have low noise and good temperature stability. (b) Cermets film Resistors

ELT-114 Electrical Essentials & Networks Page 68 These resistors are made by depositing a layer of carbon or metal alloy on a ceramic rod (called substrate). These resistors are made for more precise values and greater stability for heat. These are in the shape of square or rectangle with leads as terminals and can be easily fixed on a printed circuit board. Fig.2.44Metal Oxide Resistor (c) Fusible Resistors Fusible resistors acts like a fuse in a circuit and consist of a wire wound resistor which can be burnt out easily whenever the power rating is exceeded a certain predetermined value. These resistors have value, less than 10Ω. These are used in TV sets and amplifiers to protect certain circuits. Variable Resistors Variable resistors are defined as the resistors whose resistance value can be changed from zero to specific maximum value. In order to change the value of the resistance a rotating knob, screw or sliding arm is used. Various types of variable resistors are: (a)Potentiometers (b)Rheostats (c)Trimmers Potentiometers: Potentiometers are three terminal variable resistors. The outer terminals are fixed and other central terminals are variable. It is shown in figure below: Fig.2.45Variable resistor (potentiometer)

ELT-114 Electrical Essentials & Networks Page 69 Potentiometers are used for controlling the voltage and current in a circuit. Rheostats Rheostat is also a variable resistance which is used for high voltage. It is also called as variable wire wound resistor. Rheostats are manufactured by wounding a nichrome wire on a ceramic core. A rheostat has 2 or 3 terminals and the resistance of the rheostat can be changed by moving a wiper attached to its body. It is shown in figure below: Fig.2.46 Rheostat If a rheostat is used to change the voltage then it is called as Potentiometers. Potentiometers can be used as rheostat as shown in figure below: Fig.2.47 Potentiometers as rheostat Trimmers: Trimmers are variable resistors in which resistance is varied by loosing or tightening a screw built at the body of the trimmer. Trimmers can be single turn or multi turn and resistances can vary from

ELT-114 Electrical Essentials & Networks Page 70 50Ω to 5 mega Ω in power ratings of 1/4 to 3/4 watts Trimmers are shown in figure below. Fig.2.48Trimmer Non-Linear Resistors: In non linear resistors there is no specific relationship between current and voltage across the resistance. Different types of non-linear resistors are: (a) Thermistor (b) Photo resistors (c) Varitsors Thermistors Thermistor is a temperature sensitive resistor. It has two terminals and has variable resistance. It is used to detect very small changes in temperature. Thermistors are found in both types i.e. negative temperature coefficient (NTC) type and positive temperature coefficient (PTC) type. In positive temperature coefficient type resistance, increases with the increase in the temperature In NTC type resistance decreases with the increase in the temperature. Thermistors are found in the form of beads, Probes, discs, Washers and rods as shown in figure below: Fig.2.49Thermistors Figure 2.41 Symbol

ELT-114 Electrical Essentials & Networks Page 71 NTC thermostats are prepared from cobalt, nickel, strontium and manganese dioxide. PTC thermostats are manufactured from doped Barium tantalite semiconductors. Photo Resistors Photo resistors are two terminal semi conductor devices whose terminal resistance changes with the light intensity. Materials used to develop photo resistors are called as Photoconductors. Such materials are cadmium sulphide, Cadmium selenide and lead sulphide etc. Photo resistors are shown in figure below: Fig.2.50Photo resistors When the light intensity on the surface of the photo resistors increases the no. of free carriers or hole pairs at the surface of the material increases, resulting in a decrease of resistance. When light intensity decreases, the photo resistor resistance increases. Due the variations in resistance, the photo resistors are used in many industrial applications like light meters, light activated relay control circuits, Burglar alarms, smoke detectors etc. The photo resistors are NTC type. Varitsors Varitsors are voltage dependent resistors (VDRs) i.e. the value of the resistance changes when the supply voltage changes. VDRs are used to suppress the high voltage transients which can cause harm to the devices. Varitsors are found in a large variety of packages and operating voltage ranging from 12 volts to 650 volts and can handle currents up to 2000 Amps. Varitsors are shown in figure below.

ELT-114 Electrical Essentials & Networks Page 72 Fig.2.51Varistors 2.4.3 APPLICATIONS (USES) OF RESISTORS: Resistors are used in my applications to limit the current and voltage in the circuits. Resistor shows the similar behavior at dc and ac supplies. Some of the many applications of resistors are enlisted as follows: i. In order to control or divide the voltage. ii. To control the current in the circuit. iii. In electronics circuits for wave shaping and many other applications. iv. In ampere meters and voltmeters. v. In domestic application in electric iron, bulbs, heaters etc. vi. To control the temperatures. vii. In the protection of electric circuits and systems. 2.4.4 RESISTOR COLOUR CODING: Resistor color coding is used to find the resistance value by using the different color bands found on the body of the resistor. Since the size of the resistor is very small so it is not possible to write the value of the resistance on the body of the resistor. In color coding 4 or 5 bands of various colors are printed on the body of the resistor. The value of the resistance is read by using the table and following technique. i. First band represent the first significant digits of the value of the resistor. ii. Second band represents the second significant digit of the value of the resistor. iii. 3rd band specifies the no. of zero to be assigned to 1st two significant digits found in steps 1 & 2. iv. Fourth band represents the possibility of tolerance. If its color is silver it represents 10% tolerance, if the color is gold it represents 5% tolerance and if there is no band it means 20% tolerance.

ELT-114 Electrical Essentials & Networks Page 73 Fig.2.52Resistor color coding 2.4.5 POWER RATINGS OF RESISTOR : In a properly designed circuit, apart from the value of the resistance, suitable selection of power rating is also very important. Since we know that that power dissipated in a resistor is determined by I 2R and if a lesser power rating resistor is used, it will be burnt out and circuit will stop functioning. So manufacturers are designing the resistors for proper ratings. Power rating of a resistor represents its maximum power which it can handle safely. Normally carbon resistors are designed for 1 10 , 1 8 , 1 4 , 1 2 ,2 watts wire wound resistors are made from 1 4 watts to 200 watt values. By increasing the size of the resistor, the power handling ability can be increased. 2.5 BATTERIES: Batteries are the most common power source for basic handheld devices to large scale industrial applications. A battery can be defined as; it is a combination of one or more electrochemical cells that are capable of converting stored chemical energy into electrical energy.

ELT-114 Electrical Essentials & Networks Page 74 2.5.1 TYPES OF D.C SOURCES: There are two types of currents i.e. ac and dc. DC means direct current and it has only one direction of flow i.e. from the positive terminal to the negative terminal of the source or vice versa. DC can be obtained from the following sources. (i) Cells A cell is a device which produces dc voltage by the chemical reaction. (ii) Batteries When different cells are combined a battery is farmed. (iii) Generator It produces dc by converting mechanical energy into electrical energy. (iv) Power Supplies Power supplies also provide dc. In power supplies ac is converted to dc through rectification. 2.5.2 TYPES OF CELLS: A cell is a device which produces direct current due to the internal chemical reactions. There are two basic types of cells. (i) Primary cell (ii) Secondary cell Primary Cell A primary cell is defined as a cell which cannot be recharged once it is discharged. The basic principle of cell is that when two dissimilar metals are called Electrodes are placed in an electrolyte; EMF is produced due to the chemical reaction. The EMF continues to remain available until the electrolyte is fully utilized and converted into some other shape. In a primary cell it is not possible to reverse the chemical action to bring the electrolyte to its original state. Examples of primary cells are Mercury Cell, Silver Oxide Cell etc. Secondary Cell A secondary cell is one which can be charged once it is discharged. In the secondary cell the chemical reaction which takes place between the electrolyte and electrode during the discharging can be reversed by passing a current through the cell in the opposite direction. Examples of secondary cell are Nickel Cadmium Cell, Lead Acid Batteries etc.

ELT-114 Electrical Essentials & Networks Page 75 Comparison of Primary and Secondary Cells Table 2.8 Primary Cells Secondary Cells It cannot be recharged. It can be recharged. It is light in weight. It is heavy in weight. Its life is short. Its life is long. Its output is small. It has more output voltage. It has large internal resistance. It has small internal resistance. Its price is low. Its price is high. Popular Primary Cells 1. Mercury Cell Mercury cell is a primary cell. It is used with a high current density with a uniform discharge characteristics are required. Its internal resistance is low and remains constant. Mercury cell consists of a cathode which is made from compressed mercuric oxide mixed with a small percentage of graphite. The anode is made from a purified zinc powder. KOH is used as electrolyte. Mercury cell is made in the shape of flat, round cylinder and small button shapes. It is shown in figure below. Fig.2.53Mercury Cell

ELT-114 Electrical Essentials & Networks Page 76 Mercury cell is used where uniform discharge characteristics are required. These are used in radios, Electric watches, Instruments, Computers and measuring devices etc. It provides output in volts 1-2 volts. 2. Silver Oxide Cell Silver oxide cell is a primary cell. It consists of depolarizing cathode and a powdered zinc anode. KOH or NaOH is used as Electrolyte. The depolarizing cathode comprises of AgO2 and manganese dioxide MnO2. The cathode is made depolarizing to avoid the hydrogen ions which are gathered at the silver plate during the chemical reaction. To avoid this gathering of hydrogen ions manganese dioxide is mixed with AgO2. It improves the life of the cell. Silver oxide cells are made in the form of buttons or discs and provide few volts output 2-3 volts. Silver oxide cells are used in hearing and reference voltage sources, Electronic instruments and watches etc. Fig.2.54 Popular Secondary Cells 3. Nickel Cadmium Cell Nickel Cadmium is a reversible cell or a secondary cell. The open circuit voltage provided by the cell is 1.25 to 1.5 volts. It is used for high current density applications and is highly reliable for long term applications. Nickel cadmium cell is available in both sealed and non-sealed designs but the sealed constructions are common. It is shown in figure below. Nickel cadmium cell are used in portable power tools, alarm systems, and portable radio or television equipments.

ELT-114 Electrical Essentials & Networks Page 77 Fig.2.55 -Nickel Cadmium Cell The positive electrode is Ni and negative electrode is Cd. KOH is used as Electrolyte. The chemical equation for NiCd cell can be written as follows. The electrolyte KOH does not appear in the chemical reaction. The reason is that the function of this electrolyte is just to act as a conductor for the transfer of OH– ions. NiCd cell is a true storage cell with a reversible chemical reaction for recharging that can be cycled up to 1000 times. It should be noted that a new NiCd battery may need charging before use. 2.5.3 LEAD ACID BATTERY: Lead acid cell is used when high values of load current are necessary. The electrolyte is dilute solution of sulphuric acid H2So4. The lead acid cell is a secondary cell or storage cell which can be recharged. The charge and discharge cycle can be repeated many times to restore the output voltage as long as the cell is in good physical conditions. One cell has a nominal output of 2.1V but lead acid cells are often used in a series combination of three for a 6V battery and six far a 12 volt battery. In lead acid battery positive and negative electrodes consists of a group of plates welded to a connecting strap. The plates are dipped in the electrolyte consisting of 8 parts of water to 3 parts of concentrated sulphuric acid. It is shown in figure 2.56. Each plate is a grid of framework, made of lead antimony alloy. This construction enables the active material, which is Charge 3 2 2 Discharge 2Ni(oH) + Cd 2Ni(oH) + Cd(oH)

ELT-114 Electrical Essentials & Networks Page 78 lead oxide to be pasted into the grid. In manufacturing of the cell, a forming charge produces the positive and negative electrodes the negative electrode is spongy lead (Pd). The electrolyte i.e. H2SO4 is a combination of hydrogen and sulphate ions. When the cell discharges, lead peroxide from the positive electrode combines with the hydrogen ions to form water and with sulphate ions to form lead sulphate. The lead sulphate is also produced by combining lead on the negative plate with sulphate ions. Therefore, the net result of discharge is to produce more water, which dilutes the electrolyte and to form lead sulfate on the plates. As discharge continues, the sulfate fills the pores of the grids, retarding circulation of acid in the active material. Lead sulphate is the powder often seen on the outside terminals of the old batteries. On charge the external dc source reverses the current in the battery. The reversed direction of ions flowing in the electrolyte results in a reversal of the chemical reactions. Now the lead sulphate on the positive plate reacts with the water and sulphate ions to produce lead per oxide and sulphuric acid. This action reforms the positive plate and makes the electrolyte stronger by adding sulphuric acid. This chemical reaction for discharging and charging is shown below: The state of the discharge of a lead acid is generally checked by measuring the specific gravity of the electrolyte. Specific gravity reading is taken with a battery hydrometer. Charge 2 2 4 4 2 Discharge Pb +Pbo + 2H So 2PbSo + 2H O

ELT-114 Electrical Essentials & Networks Page 79 Fig.2.56 Lead Acid Cell 2.5.4 SOLAR CELL: A solar cell works on the principle called photo voltaic effect. A solar cell consists of two layers of different materials. One layer is photo sensitive that is when light energy falls on it, emits electrons. The other layer is capable of absorbing the electrons. The layer which emits electron i.e., losses the negative charge becomes positive and acts as a positive electrode. On the other hand the layer which accepts electrons becomes negative and acts as negative electrode. In this way by these two electrodes a cell is formed which is called as Solar Cell. A silicon solar cell is made of P-type and N-type crystals or diode which is sealed and has a glass window on the top to collect the solar light. Ptype surface, the top surface of the solar cell is made very thin so that it can easily reach the PN junction. When light energy falls on the surface of the cell then electrons gains the energy and leave their parent atoms and cross the junction. In this way one side of the junction becomes positive electrode and other side becomes negative electrode. A potential difference is established and it provides output like cell. Indium Arsenide (InAs), Cadmium Arsenide (CdAs) is the materials which are widely used in solar cells. A solar cell provides 0.26 volt. In order to get higher voltage many cells are connected in series.

ELT-114 Electrical Essentials & Networks Page 80 Fig.2.57 Solar Cell 2.5.5 INTERNAL RESISTANCE OF CELL : The resistance offered by a cell is called as Internal Resistance. Expressed as “ri” Every cell has a certain internal resistance ri which depends upon the construction of the cell. A good cell should have minimum internal resistance. When load is connected to a cell voltage drop is developed across the internal resistance and this potential drop reduces the voltage across the load. The internal resistance of cell can be measured by the simple experimental arrangement shown in figure 2.58. Fig.2.58 internal resistance of Cell

ELT-114 Electrical Essentials & Networks Page 81 The cell is connected in series with the resistance R as shown in figure 2.58. Ampere meter A may be connected in series with resistance R and a voltmeter V may be connected across the two terminals of the battery. First of all we measure the value of the voltage of the battery and say it is E. Now observe the value of the voltage at the terminal of the battery will reduce and say it is V. The internal resistance of the cell may be obtained by the relation. 2.5.5 CONSTANT VOLTAGE AND C CURRENT SOURCE: Parallel combination of cells as constant voltage source: Similar cells can be combined in parallel to work as constant voltage source. In this case we can meet the higher load current demand. To achieve this combination all positive terminals are connected to each other and all negative terminals are connected to each other. One positive terminal and one negative terminal is taken out to connect to the load. In parallel combination of cells the net current is the sum of the individual currents of each and the output voltage is the same as the voltage of the individual cell. Fig.2.59 Parallel combination of Cells Series combination of cells as constant current source: If the load demand is higher voltage then required numbers of cells are connected in series. In series combination, the negative terminal of first cell is connected to the positive terminal of the second cell and so on. Output load is connected to the positive terminal of the first cell to the negative terminal of the last. If two cells of 2V each are connected in series then the load terminal i E - V r = I

ELT-114 Electrical Essentials & Networks Page 82 output will be 4 volts. The current is the same in all the cells and across the load. Fig.2.59 Series combination of Cells

ELT-114 Electrical Essentials & Networks Page 83 Multiple Choice Questions Q.1 The _______ law states that potential difference is directly proportional to current. (a) Coulomb’s (b) Ohm's (c) Kirchhoff's voltage (d) Lenz's Q.2 According to Ohm's law (a) Q = CV (b) V = IR (c) R= ρ L / A (d) B=Ø/A Q.3 According to Ohm's law, with the increase in potential difference current _______ (a) Increases (b) Decreases (c) Remains constant (d) Fluctuates Q.4 When current flows through a circuit, having 20Ω resistance, the amount of applied voltage is 100v then the current is: (a) 4A (b) 5A (c) 7A (d) 12A Q.5 The resistance is directly proportional to the _______ of the conductor. (a) Width (b) Breadth (c)Thickness (d) Length Q.6 Resistance is____ proportional to the cross section area of conductor. (a) Directly (b) Inversely (c) Not (d) Any of above Q.7 The resistance of a conductor depends on the _______. (a) Friction (b) Collision (c) Colour (d) Temperature Q.8 The Greek letter "Rho" denotes the _______ (a) Conductivity (b) Resistivity (c) Malleability (d) Permeability Q.9 Conductors _______ current to flow easily. (a) Allows (b) stop (c) Block (d) Conduct Q.10 Conductors have _______ number of electrons in their structure. (a) Small (b) Random (c) Large (d) Swift Q.11 The ability to conduct is _______. (a) Electricity (b) Conductivity (c) Resistivity (d) All of above Q.12 The opposition offered to free electrons is _______.

ELT-114 Electrical Essentials & Networks Page 84 (a) Conductance (b) Current (c) Torque (d) Resistance Q.13 Resistance adds up in _______. (a) Series (b) Parallel (c) Series parallel (d) any of above Q.14 P.D stands for _______. (a) Power Display (b) Power driven (c) Potential difference (d) Proportional difference Q.15 In series circuit of resistances, the voltage _______ in each resistor. (a)Increases (b) Decreases (c) Drops (d) Constant Q.16 Current remains _______ in series circuits. (a) Increasing (b) decreasing (c) Constant (d) Oscillating Q.17 Voltage remains _______ in parallel circuits. (a) Increasing (b) decreasing (c) Divides (d) constant Q.18 Current _______ in parallel circuit of resistances. (a) Increases (b) decreases (c) Divides (d) Constant Q.19 The rate of doing work is called _______ (a)Energy (b) Joule (c) Voltage (d) Power Q.20 The relationship for power is P = _______ (a) C×V (b) Q/t (c) IR (d) VI Q.21 1 hp = _______ (a) 742W (b) 746W (c) 748W (d) 750W Q.22 An amount of 100J energy is used for 5sec. Determine the power in Watts. (a) 30W (b) 20W (c) 40W (d) 15W Q.23 The ability of a body to do work is called _______. (a) Power (b) Potential (c) Newton (d) Energy Q.24 The algebraic sum of all voltage drops in a closed path is zero. This statement is

ELT-114 Electrical Essentials & Networks Page 85 (a) KVL (b) KCL (c) KBL (d) BCL Q.25 The total current into a junction is equal to the total _______ out of that junction. (a) Voltage (b) current (c) Capacitance (d) inductance Q.26 In the branch current method __ voltage and current laws are used. (a) Lenz's (b) Ohm's (c) Faraday's (d) Kirchhoff’s Q.27 In node voltage method _______ are founded at each node. (a) Charges (b) Electrons (c) Voltage (d) Currents Q.28 Loop currents are _______ quantities. (a) Analytical (b) Mathematical (c) Differential (d) Positive Q.29 There are _______ basic types of resistors. (a) 2 (b) 4 (c) 6 (d) 8 Q.30 The _______ resistor does not change its value with applied voltage. (a) Linear (b) Constant (c) Non-Linear (d) Variable Q.31 The resistor whose value cannot be changed is called a _____ resistor. (a) Variable (b) Fixed (c) Positive (d) Neutral Q.32 _______ is a variable resistor. (a) Rota meter (b) Rheostat (c) Both a & b (d)none of above Q.33 The thermistor is _______ device. (a) Linear (b) Variable (c) Non-Linear (d) Fixed Q.34 LDR stands for _______. (a) Light dependent resistor (b) Light-dividing resistor (c) Light differential resistance (d) Light-doped rheostat Q.35 DC source is basically of _______ types. (a)Two (b) Four (c) Six (d) Eight Q.36 Mercury cell is _______ cell. (a) Primary (b) Secondary

ELT-114 Electrical Essentials & Networks Page 86 (c) Linear (d) Constant Q.37 _______ cell cannot be recharged. (a) Primary (b) Secondary (c) Variable (d) Constant Q.38 Every cell has a certain _______ resistance denoted as ri. (a) External (b) Internal (c) Extrinsic (d) Intrinsic Q.39 The combination of cells is called _______. (a) Battery (b) Adapter (c) Voltage level (d) Current level Q.40 In order to provide higher currents, cells are connected in _______. (a) Series (b) Parallel (c) Cascaded (d) Any of above ANSWER KEY 1.(b) 2. (b) 3.(a) 4.(b) 5.(d) 6.(b) 7.(d) 8.(b) 9.(a) 10.(c) 11.(b) 12.(d) 13.(a) 14.(c) 15.(c) 16.(c) 17.(d) 18.(c) 19.(d) 20.(d) 21.(b) 22. (b) 23.(d) 24.(a) 25.(b) 26.(d) 27.(c) 28.(b) 29.(a) 30.(a) 31.(b) 32.(b) 33.(c) 34.(a) 35.(b) 36.(a) 37.(a) 38.(b) 39.(a) 40.(b)

ELT-114 Electrical Essentials & Networks Page 87 Short Questions 1. Define Ohm's law 2. What is the resistance of a lamp if a current of 150mA flows through the lamp when 6 volts is applied to its terminals? 3. Describe the laws of resistance. 4. Define specific resistance. 5. Define conductor. 6. Define conductivity. 7. Define resistance 8. Explain temperatures co-efficient of resistance 9. Describe the resistance in series. 10. Describe the resistance in parallel. 11. What is the total resistance of four resistors connected in series if their individual values are 1MΩ, 1.5MΩ, 150KΩ and 50,000 KΩ. 12. Two resistors of 3.1Ω and 7.2Ω respectively are connected in parallel. Find the equivalent resistance. 13. Define power. 14. Define Watt. 15. Define energy. 16. Calculate the power of a 120V energy source that delivers 15A of current. 17. Calculate the voltage required to develop 10.5 KW with 5A current. 18. Define KCL. 19. Define KVL. 20. In any closed loop the algebraic sum of the EMFs applied is equals to the algebraic sum of the voltage drops in the elements. 21. List types of resistors. 22. A resistor has the following order of color codes: red, red, red, gold. 23. Describe power rating of resistor. 24. Name type of DC sources. 25. Describe series combination of cells. 26. Describe parallel combination of cells.

ELT-114 Electrical Essentials & Networks Page 88 Long Questions 1. Describe ohm’s law and prove the equation V = IR 2. Prove Laws of Resistances. 3. Explain the effects of temperature on resistance. 4. Explain resistances in series , in parallel and in series parallel combination. 5. Explain volt division rule and current division rule with examples. 6. Enlist the types of linear resistors and explain any one of them in detail. 7. Enlist the types of variable resistors and explain any one of them in detail. 8. Enlist the types of non linear resistors and explain any one of them in detail. 9. How you can explain resistor color coding with examples. 10. Compare primary and secondary cells. 11. Describe the structure of mercury cell. Write down its working and its uses. 12. Describe the structure of silver oxide cell. Write down its working and its uses. 13. Describe the structure of nickel cadmium cell. Explain its working with the help of charging and discharging equation and its uses. 14. Describe the structure of lead acid battery. Explain its working with the help of charging and discharging equation and its uses. 15. How you can explain cells combination in series, parallel and series parallel. 16. How you can explain solar cell.

ELT-114 Electrical Essentials & Networks Page 89 Chapter 03 Magnetism & Electromagnetism OBJECTIVES After completion of this chapter students will be able to: 1. Learn about magnetism, magnetic line of force, flux, flux-density, permeability, Reluctance and their units 2. Learn Properties of magnetic lines of force & types of magnets. 3. Understand Magnetic properties of materials (Ferro, Para and diamagnetic) magnetic induction. 4. Understand Electromagnetism. 5. Learn Electromagnetism, M.M.F. (AT) field intensity (H =AT/L) ampere turns/meter. 6. Understand & draw B-H curve and magnetic Hysteresis. 7. Learn Electromagnetic induction. 8. Understand Magnetic field around a current carrying conductor and solenoids cork screw and left hand rules. 9. Learn Force between two magnetic fields and motor action. 3.1 MEGNETISM Magnet Magnet is a piece of metal which can attract iron or materials made with iron. When a bar magnet is freely suspended it points in the direction of North and South. The side which points towards the north is called as North Pole and the side which points towards south is called as South Pole. Two similar poles repel each other and opposite poles attract each other. There are two types of magnet. 1. Natural Magnet 2. Artificial Magnet Magnetism

ELT-114 Electrical Essentials & Networks Page 90 It is the property of a magnet to attract iron or things made with iron towards itself. Magnetic Field The region or space around a magnet where the effects of magnetism on a test magnet or a compass needle can be detected is called a magnetic field. 3.1.1 Lines of force, flux, flux density, permeability, reluctance and their units: Magnetic Lines of Force The magnetic lines of forces are a path in a magnetic field along which a test magnet moves in a magnetic field. Fig.4.1 Magnetic Lines of Forces Flux (ϕ) Flux means magnetic flux. The total number of magnetic lines of force passing through a particular point is called as flux. It is denoted by φ. Its unit is Weber. It is equal to 108 magnetic lines of force. Flux Density (B) Number of magnetic lines of force passing through per unit area is called as flux density. It is represented by B. Its unit is Weber/m². 1 Weber/m² is also called as 1 Tesla. Fig.3.2 Flux Density Permeability B A

ELT-114 Electrical Essentials & Networks Page 91 The ratio of the magnetic flux density (B) to the magnetizing force (H) is called as permeability of the magnetic material and is denoted by µ. µ = The permeability of a material shows its magnetizing ability and depends on the nature of the material. The greater the value of permeability, more easily magnetic field can be produced in that material .We normally relates the permeability of a material relative to the permeability of free space. The permeability of free space is denoted by µo. The relative permeability is represented by µr Since µr is the ratio of two identical quantities so it has no units. Reluctance (ℛ) Reluctance is analog of resistance in the electric circuits. It is represented by ℛ. It is opposition to the magnetic flux. ℛ = Reluctance = MMF φ The unit of reluctance is ampere-turns per Weber (AT/Wb). 3.1.2 PROPERTIES OF MAGNETIC LINES OF FORCE: i. The magnetic lines of force start from North Pole and end at South Pole. ii. The no. of lines of force at a point represents the strength of the field. Larger no. of lines shows a strong and smaller lines corresponds a weak field. iii. No two magnetic lines of force intersect each other. iv. The magnetic lines of force are invisible. v. If magnetic lines of force try to contract each other, then they start from north pole and ends at south pole i.e. they show different poles. vi. Magnetic lines of force try to expand, they represent similar poles. 3.1.3 TYPES OF MAGNET: Magnets are of following types: 1. Natural Magnets: Natural magnets are found in nature in the form of stones. For example magnetite Fe3O4 has the magnetic properties. Our earth is also supposed to a very large magnet. 2. Permanent Magnets: r o

ELT-114 Electrical Essentials & Networks Page 92 These are made from hard magnetic materials such as cobalt steel magnetized by induction in the manufacturing process. A very strong field is needed for induction in these materials. When the magnetizing field is removed residual induction makes the material a permanent magnet. A common PM material is alnico, a commercial alloy of aluminum, nickel and iron with cobalt, copper and titanium added to produce about 12 grades. The alnico V grade is often used for PM loud speakers. Commercial permanent magnets will last indefinitely if they are not subjected to high temperatures, to physical shock, or a strong demagnetizing field. A permanent magnet does not become exhausted with use, as its magnetic properties are determined by the structure of the internal atoms and molecules. Electromagnets: Electromagnets are temporary magnets. If a current is passed in a wire conductor then a magnetic field is produced around the wire. Consider a wire wrapped in the form of coil as shown in figure below, the current and its magnetic field become concentrated in a smaller space, resulting in a stronger field. Fig.3.4 Arrangement for Electromagnet The direction of the north and South Pole of an electromagnet is determined by right hand rule. Electromagnets are widely used in different application. Common applications of electromagnets are electric bell, relays, induction coils, transformers and measuring instruments. 3.1.4 MAGNETIC PROPERTIES OF MATERIALS: Different properties of magnetic materials are as follows: i. Two similar poles of a magnet repel each other and different poles attract each other.

ELT-114 Electrical Essentials & Networks Page 93 ii. When a magnet is freely suspended in air it points in the direction of north and south. The side which is pointing in the direction of north is called as North Pole and the side which point in the direction of South is called as South Pole. iii. When a magnet is broken in to pieces, at the center the separate pieces become independently. 3.1.5 TYPES OF MAGNETIC MATERIALS: Materials can be classified as magnetic and non-magnetic Iron, Nickel and Cobalt are magnetic materials and are easily magnetized. Non-magnetic materials cannot be magnetized. Examples are air, glass, wood, paper, plastic and rubber etc. Magnetic materials can be further divided into three types: i. Diamagnetic material ii. Paramagnetic materials iii. Ferromagnetic materials Diamagnetic Materials These include bismuth, antimony, Copper, Zinc, and Mercury, gold and silver. The permeability is less than 1. They become weekly magnetized in the direction opposite to the magnetizing field. The basics of all the magnetic effects are the magnetic field associated with electric charges in motion. The atoms of each substance consist of electrons which revolve around the nucleus and at the same time rotating and spinning about its own axis. These rotations and spin both give rise to magnetic field. Since the atom consists of many electrons, so every electron will have its own magnetic field. The directions of the magnetic fields produced by these electrons are random. These fields may cancel each other or these fields can build up each other. If the magnetic fields produced by the atoms cancel each other effect it is called as Diamagnetic Material. Paramagnetic Materials These materials include aluminum, platinum, manganese and chromium. The permeability is slightly more than 1.In paramagnetic materials the magnetic fields produced due to orbital motion of electrons and spin of electrons support each other. They become weekly magnetized in the same direction as the magnetizing field.

ELT-114 Electrical Essentials & Networks Page 94 Ferromagnetic Materials Ferromagnetic materials include iron, steel, nickel, cobalt, and commercial alloys such as alnico and Perm alloy. These materials become strongly magnetized in the same direction as the magnetizing field with high values of permeability from 50 to 5000. In ferromagnetic materials the orbital motion and spin motion produces magnetic field and this field is greatly strengthened by other atoms. 3.1.6 MAGNETIC INDUCTION: The electrical effect of one body on another without any physical contact between them is called Induction. For example a permanent magnet can induce an un-magnetized iron bar to become a magnet without the two touching. The iron bar then becomes a magnet as shown in figure below. It is due to the fact that the magnetic lines of force gathered by the permanent magnet make the internal molecular magnets in the iron bar line up in the same direction, compared with the random directions in the unmagnified iron. The magnetized iron bar then has the magnetic poles at the ends as a result of the magnetic induction. It should be noted that the induced poles in the iron have opposite polarity from the poles of the magnet. Since opposite poles attract so the iron bar will be attracted towards the magnet. A magnet attracts any magnetic material towards itself due to Induction. The two bars shown in above figure are not touching; even then the iron bar is in the magnetic flux of the permanent magnet. It is the invisible magnetic field that links the two magnetic fields. This idea of magnetic flux extending outward from the magnetic poles is the basis for many inductive effects in the ac circuits. 3.2.1 ELECTROMAGNETISM: When a current passes through a conductor, a magnetic field is established around the conductor. This magnetic field is surrounded along its full length. It can be verified by a simple experiment as shown below.

ELT-114 Electrical Essentials & Networks Page 95 Fig.3.6 arrangement for electromagnet Consider a current carrying conductor wire and around this wire iron fillings are aligned in concentric rings as shown in the above figure. Since the magnetic field is invisible, however its effects can be seen easily. This effect of producing magnetic field by the current passing through the conductor is called as Electromagnetism. 3.2.2 MAGNETO- MOTIVE FORCE (M.M.F) : The magneto motive force is analog of electromotive force for electric circuits. Magneto motive force is a force which produces magnetic flux in a magnetic circuit. Mathematically MMF=NI Where, I represents current and N is the number of turns. Fig.3.3Magneto motive Force (MMF) 3.2.3 MAGNETIC FIELD INTENSITY (H=AT/L) : The magnetizing force is given by the formula MMF=NI Its unit is Ampere Turns. The ampere turns or MMF specifies the magnetizing force, but the intensity of the magnetic field depends how long the coil is. At any point in the space, a specific value of the ampere turns must produce less field intensity for a long coil than for a short coil that concentrates the same NI.

ELT-114 Electrical Essentials & Networks Page 96 The magnetic field intensity H is given by This formula is for solenoid. H= Intensity at the center of air core. With iron core H is the intensity through the entire core. =Length of the ends of the core or distance between poles at the ends of core. 3.2.4 & 3.2.5 B-H CURVE: The graph between the B and H for a coil or solenoid is called as B-H curve. It shows how much flux density B results from increasing the amount of field intensity H. In order to understand the plotting of B-H curve following simple experimental arrangement is described. Consider the following solenoid which is energized with a variable power supply V. I R V = 0.2m (Length of solenoid is 0.2m) 100 turns Fig.3.7 arrangement for electromagnet Let N=100 turns and vary the voltage V which will result in the variation of the current I. Consider a soft iron for which we get the following table. Table 4.1 Sr. No Volt R Ω I=V/R Amps. N (Turns) NI (Ampere Turns) H= NI/L µr µ0 B= µ0 µr H 1 20 10 2 100 200 1000 100 1.26x10-6 0.126 2 40 10 4 100 400 2000 100 1.26x10-6 0.252 NI(Ampere Turns) H (Meters) NI H

ELT-114 Electrical Essentials & Networks Page 97 3 60 10 6 100 600 3000 100 1.26x10-6 0.378 4 80 10 8 100 800 4000 85 1.26x10-6 0.428 5 100 10 10 100 1000 5000 70 1.26x10-6 0.441 It is noted that as the value of V increases the current in the coil increases resulting in the increase of NI. If NI increases, then H increases. Since flux density B is related to H by B = µH or B= µ0 µr H so by increasing H, B increases. B depends on H and permeability of the iron. It should be noted that permeability decreases for the highest values of H. With less µ, the iron core cannot provide proportional increases in B for increasing values of H. Now it is seen that for values of H above 4000 AT/M, approximately the values of B increases at a much slower rate and if we plot a graph between B & H, this now make the curve relatively flat. The effect of little change in the flux density, when field intensity increases is called saturation. So at the flat area of the curve, the iron core gets saturated with magnetic lines of induction. Fig.3.8 B-H curve The above curve for air core and iron core can be generalized as shown in Fig 3.9: